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A052722
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Expansion of e.g.f. (1 - 2*x - sqrt(1-4*x))^2 * (1 - sqrt(1-4*x))/8.
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9
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0, 0, 0, 0, 0, 120, 3600, 100800, 3024000, 99792000, 3632428800, 145297152000, 6351561216000, 301699157760000, 15487223431680000, 854894733428736000, 50516506975334400000, 3182539939446067200000, 212985365178313728000000
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OFFSET
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0,6
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LINKS
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FORMULA
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D-finite with recurrence: a(0) = a(1) = a(2) = a(3) = a(4) = 0, a(5)=120, a(n+3) = (9+7*n)*a(n+2) + (14 - 19*n - 13*n^2)*a(n+1) - (20 + 22*n - 2*n^2 - 4*n^3)*a(n).
G.f.: 5!*x^5*hypergeometric2F0([5/2, 3], [], 4*x).
E.g.f.: (1/2)*(1 - 5*x + 5*x^2 - (1 - 3*x + x^2)*sqrt(1-4*x)). (End)
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MAPLE
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spec := [S, {C=Union(B, Z), B=Prod(C, C), S=Prod(B, B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[((1-2x-Sqrt[1-4x])^2 (1-Sqrt[1-4x]))/8, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 30 2021 *)
Table[If[n<5, 0, 10*(n-2)!*Binomial[n-3, 2]*CatalanNumber[n-3]], {n, 0, 30}] (* G. C. Greubel, May 28 2022 *)
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PROG
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(SageMath)
if (n<5): return 0
else: return 10*factorial(n-2)*binomial(n-3, 2)*catalan_number(n-3)
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CROSSREFS
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Cf. A052711, A052712, A052713, A052714, A052715, A052716, A052717, A052718, A052719, A052720, A052721, A052723.
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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